Demodulation using serial localization with indecision

ABSTRACT

A receiver includes a constellation processing module and a plurality of demodulation stages. The constellation processing module groups points of a constellation associated with a transmitted signal into a plurality of subsets, were at least two adjacent ones of the subsets have one or more common constellation points so that the at least two adjacent subsets overlap. The constellation processing module also determines a centroid-based value for each of the subsets of constellation points and groups the centroid-based values into one or more sets. Each of the demodulation stages except for the last demodulation stage localizes a search for a final symbol decision using the set of centroid-based values input to or selected by the demodulation stage as constellation points. The last demodulation stage determines the final symbol decision using the subset of constellation points input to or selected by the last demodulation stage.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of patent application Ser. No.12/549,132, filed on Aug. 27, 2009, which is incorporated by referenceherein in its entirety.

TECHNICAL FIELD

The present invention generally relates to demodulation, and moreparticularly relates to demodulation based on serial localization withindecision.

BACKGROUND

Demodulation involves extracting an original information-bearing signalfrom a signal which is modulated in accordance with a particularconstellation and transmitted over a channel. The complexity of thedemodulation process increases significantly for very large signalconstellations. Relatively large signal constellations such as 16-, 32-and 64-QAM (Quadrature Amplitude Modulation) have been adopted in EDGE(Enhanced Data Rates for GSM Evolution), HSPA (High Speed PacketAccess), LTE (Long Term Evolution) and WiMax (Worldwide Interoperabilityfor Microwave Access). In HSPA, multi-code transmission creates evenlarger effective constellations. Also, MIMO (Multiple-Input,Multiple-Output) schemes with two or more streams have been adopted inHSPA, LTE and WiMax. MIMO implementations also yield relatively largeeffective constellations. Demodulation complexity further increases whenany of these techniques occur in combination, e.g. multi-code and MIMO.

The ideal demodulation scheme is MLD (Maximum Likelihood Detection).However, the complexity of MLD increases substantially due to the sizeof the modulation constellation and/or because of the exponentialeffects of MIMO or multi-codes to the point where MLD becomesimpractical. Less complex solutions are available such as spheredecoding (SD), where the demodulator tries to approximate theperformance of MLD, but limits its search for the best solution to asubset of all possible transmitted signals, and where the subset isdescribed by a sphere. A key step in SD is the triangular factorizationof the channel matrix. This step simplifies the identification ofcandidate solutions in the sphere.

Another conventional demodulation technique is ITS (Iterative TreeSearch) detection for MIMO QAM. ITS can be viewed as an alternative toSD. Like SD, ITS exploits the triangular factorization of the channel.Unlike SD, ITS uses the M-algorithm for reducing the search for the bestcandidate. ITS breaks down the search further, by dividing the QAMconstellation in its four quadrants, and representing each quadrant byits centroid in intermediate computations. The selected quadrant itselfis subdivided again into its 4 quadrants, and so on. This results in aquaternary tree search. Other conventional approaches give particularattention to the additional error introduced by the use of the centroidsinstead of true symbols. The error is modeled as Gaussian noise whosevariance is determined and incorporated in likelihood computations.However, a tight connection is typically made between the centroidrepresentation and the bit mapping from bits to symbols. That is, if aso-called multi-level bit mapping is employed, then identifying aquadrant is equivalent to making a decision on a certain pair of bits.Such constraints place a restriction on bit mappings, restricting thedesign of subsets.

SUMMARY

Demodulation is performed in a series of stages. Each stage attempts tofurther localize the search for a solution for the benefit of the nextstage, based on input from the previous stage. The demodulator structureis referred to herein as serial localization with indecision (SLI). SLIis a lower complexity alternative to MLD, where MLD coincides with jointdemodulation (JD) for MIMO environments. Viewed in isolation, a givenSLI demodulation stage can be quite indecisive, but makes progress andavoids an irreversible wrong decision. A given demodulation stagelocalizes the solution by inputting a subset representative of theconstellation and outputting a further reduced subset. Each stage makesa choice among candidate reduced subsets. Indecision arises fromrepresenting the modulation constellation with overlapping subsets.Indecision is beneficial in a multi-stage structure, because indecisiondiscourages an irreversible bad decision in an early stage.

According to an embodiment of a method for demodulating a receivedsignal corresponding to a transmitted signal carried over a channel, themethod includes grouping points of a constellation associated with thetransmitted signal into a plurality of subsets, at least two adjacentones of the subsets having one or more common constellation points sothat the at least two adjacent subsets overlap. A centroid-based valueis determined for each of the subsets of constellation points and thecentroid-based values are grouped into one or more sets for input to ademodulator having a plurality of stages. The received signal isdemodulated using the demodulator. Each of the stages except for a lastone of the stages localizes a search for a final symbol decision usingthe set of centroid-based values input to or selected by the stage asconstellation points. The last stage determines the final symboldecision using one of the subsets of constellation points input to orselected by the last stage.

Of course, the present invention is not limited to the above featuresand advantages. Those skilled in the art will recognize additionalfeatures and advantages upon reading the following detailed description,and upon viewing the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a block diagram of an embodiment of a receiverincluding a multi-stage SLI demodulator and a constellation processingmodule.

FIG. 2 illustrates a block diagram of an embodiment of a two-stage SLIdemodulator.

FIG. 3 illustrates a diagram of an embodiment of overlappingconstellation subsets for use by a multi-stage SLI demodulator.

FIG. 4 illustrates a diagram of an embodiment of overlapping ASKconstellation subsets for use by a multi-stage SLI demodulator.

FIG. 5 illustrates a block diagram of another embodiment of a two-stageSLI demodulator.

FIG. 6 illustrates a block diagram of an embodiment of an i-th stage ofa multi-stage SLI demodulator.

FIG. 7 illustrates a block diagram of an embodiment of an N-stage SLIdemodulator.

FIG. 8 illustrates a diagram of an embodiment of overlapping QAMconstellation subsets for use by a multi-stage SLI demodulator.

FIG. 9 illustrates a diagram of another embodiment of overlapping QAMconstellation subsets for use by a multi-stage SLI demodulator.

DETAILED DESCRIPTION

FIG. 1 illustrates an embodiment of a wireless transmitter 100 incommunication with a wireless receiver 110 over a channel 120. Thereceiver includes a baseband processor 130 and a constellationprocessing module 140 and a multi-stage SLI demodulator 150 included inor associated with the baseband processor 130. The constellationprocessing module 140 groups points of a constellation associated with atransmitted signal into a plurality of subsets, e.g., subsets of ASKconstellation points, QAM constellation points, etc. At least twoadjacent subsets have one or more common constellation points to ensurethat these adjacent subsets overlap. In some embodiments, all adjacentsubsets have one or more common constellation points to ensure that alladjacent subsets overlap. In each case, the constellation processingmodule 140 also determines a centroid-based value for each of thesubsets of constellation points and groups the centroid-based valuesinto one or more sets. The values included in each set arecentroid-based in that they may be actual centroids, approximations ofcentroids such as integer values or values quantized to a certain finiteprecision, the closest constellation point to a centroid, etc. Moregenerally, each subset is assigned a centroid-based representative,which we call a centroid from here on.

The multi-stage SLI demodulator 150 includes a plurality of stages 152,154 for performing signal demodulation in stages. Each of thedemodulation stages 152 except for the last stage 154 localizes thesearch for a final symbol decision using the set of centroid-basedvalues input to or selected by the stage 152 as constellation points.The last demodulation stage 154 determines the final symbol decisionusing a subset of the initial constellation points. This way, each ofthe demodulation stages 152 except for the last stage 154 furtherlocalizes the search for a solution using a set of the centroid-basedvalues as constellation points, reducing the overall complexity of thedemodulator. The last stage 154 outputs the final solution based on asubset of the actual constellation. The constellation processing module140 ensures that at least two adjacent subsets of constellation pointsoverlap to reduce the likelihood of demodulation errors, particularlyfor the earlier demodulation stages as will be described in more detaillater herein.

FIG. 2 illustrates an embodiment of a 2-stage SLI demodulation structure200 included in the receiver 110 of FIG. 1 for demodulating a receivedsignal r_(k). The received signal r_(k) is carried over the channel 120and originally modulated at the transmitter 100 using symbolconstellation Q. For purely illustrative purposes only, signal r_(k) ina single input single output (SISO) scenario of a signal transmissionembodiment over a noisy channel with no ISI (Inter-Symbol Interference)is given by:r _(k) =H ₀ s _(k) +v _(k)  (1)where v_(k) represents white Gaussian noise, H₀ represents the channel120, s_(k) represents the transmitted symbols and all quantities arescalar. One skilled in the art can readily expand the signal modelrepresented by equation (1) to other scenarios such as MIMO andmulti-coded transmission, where the quantities in equation (1) becomevectors and matrices. The originally transmitted signal has symbolconstellation Q of size q. The constellation processing module 140 ofthe receiver 110 groups the points of constellation Q into a pluralityof subsets in a way that ensures at least two adjacent subsets overlap.The constellation processing module 140 also determines a centroid-basedvalue for each of the subsets of constellation points and generates analternative constellation Q′ including the centroid-based values, notnecessarily belonging to Q, for input to a first stage 210 of the2-stage SLI demodulation structure 200.

The first stage 210 of the SLI structure 200 performs demodulation usingthe alternative constellation Q′. That is, the first demodulation stage210 uses the centroid-based values included in Q′ as constellationpoints. Each point in Q′ represents a subset of clustered points in Q.In one embodiment, each centroid-based value included in Q′ is theactual centroid for the points of a particular subset of Q. In anotherembodiment, the centroids are approximated as integer values. In yetanother embodiment, each centroid-based value included in Q′ is theconstellation point of Q located closest to the corresponding centroidvalue. Still other types of values may be used which are derived basedon the centroids determined from the different subsets of Q.

The first demodulation stage 210 outputs a symbol decision s′_(k)^([1]), which belongs to Q′. The second demodulation stage 220 acceptss′_(k) ^([1]) and uses s′_(k) ^([1]) to choose a localized subset Q″ ofQ as its own constellation. The decision s′_(k) ^([1]) output by thefirst demodulation stage 210 can be interpreted to be the representativeof Q″ in the first demodulation stage 210. The second demodulation stage220 outputs the final symbol decision ŝ_(k), which belongs to Q″. Thefinal symbol decision ŝ_(k) output by the second stage 220 is determinedbased on the original received signal r_(k) and subset Q″, which isselected based on the localized symbol decision s′_(k) ^([1]) output bythe first stage 210. In one embodiment, both demodulation stages 210,220 implement MLD over their respective alphabets. Alternatively, thedemodulation stages 210, 220 implement other types of demodulationschemes such as joint detection, sphere decoding, tree searching, etc.The 2-stage SLI demodulation structure 200 makes q′=|Q′| comparisons inthe first stage 210 and q″=|Q″| comparisons in the second stage 220.Complexity of the SLI structure 200 is reduced when q′+q″<q. Also, SLIhas constant complexity, unlike many suboptimal techniques whosecomplexity is a random variable.

SLI can mimic the behavior of MLD. The performance of the 2-stage SLIstructure 200 of FIG. 2 is primarily limited by that of the firstdemodulation stage 210, which in turn is determined by the choice ofsubsets. Performance suffers when no adjacent subsets overlap. Considerthe case of disjoint subsets. MLD implicitly defines a decision region(Voronoi region) around each constellation point, consisting of receivedvalues closest to that point than any other. The decision regionboundaries are polyhedrons (made up of sections of hyperplanes). Twoconstellation points x and y are neighbors if their decision regionstouch. The common part is a section of the hyperplane P(x,y) thatbisects the space according to x and y. In degenerate cases, the commonpart can become a line or a point. Now consider two adjacent subsets Xand Y of Q which are available to the first demodulator stage 210 of thetwo-stage SLI structure 200. Subsets X and Y have centroids c(X) andc(Y), respectively. Consider neighbor pair (x,y), where x belongs to Xand y belongs to Y. Suppose x is transmitted, and the first demodulationstage 210 makes an error and chooses subset Y instead of subset X. Theeffective decision boundary of the first demodulation stage 210 is thehyperplane P(c(X),c(Y)). In contrast, MLD would make the choice based onP(x,y). For the sake of comparison, MLD can be thought of as making aneffective decision between X and Y. Then the effective decision boundaryis made up of the sections P(x,y) of different nearest neighbor pairs(x,y).

FIG. 3 illustrates the effective decision boundary between adjacentsubsets X and Y in two dimensions, where the hyperplane becomes astraight line and each constellation point is represented by a circle.In contrast, the decision boundary for MLD is a piecewise straightjagged line. The discrepancy between these hypothetical decisionboundaries leads to a performance loss in SLI.

Overlapping two or more adjacent subsets smoothes the decision boundarydiscrepancy. In particular, in the two stage SLI, including nearestneighbor symbols pairs in the overlap of adjacent subsets of the firstdemodulation stage means that the first demodulation stage does not haveto make a decision about those symbols. That decision will be made inthe second stage.

With SLI, the search is further localized from one stage to the next,but the final decision is not made until the last stage. In particular,by making nearest neighbor symbols belong to multiple subsets, a laterdemodulation stage (e.g. the second stage 220 in FIG. 2) may recoverfrom an error in an earlier stage (e.g. the first stage 210 in FIG. 2).In this context, indecision is beneficial. However, ensuring adjacentsubsets overlap has a cost. In terms of complexity, q′ or q″, or both,will increase for the overlap case in comparison to the disjoint case.

FIG. 4 illustrates an exemplary embodiment of an 8-ASK constellationgrouped into three subsets. The 8-ASK constellation is given by:Q={−7,−5,−3,−1,+1,+3,+5,+7}  (2)The three overlapping subsets shown in FIG. 4 have centroids given by:Q′={−4,0,+4}  (3)The overlap means that the second demodulation stage 220 of the SLIstructure 200 of FIG. 2 can often recover from a bad decision by thefirst demodulation stage 210. The two outer subsets shown in FIG. 4 areoffsets of one another, and the offset is equal to the centroiddifference. SLI complexity can be further reduced by accounting for thehighly structured nature of these subsets. Of course, less structuredsubsets can also be used with SLI.

FIG. 5 illustrates another embodiment of a 2-stage SLI demodulationstructure 500 for demodulating signal r_(k). The 2-stage SLI structure500 shown in FIG. 5 is similar to the one shown in FIG. 2, except it istailored to the highly structured nature of the ASK constellationsubsets shown in FIG. 4. The constellation input to or selected by thefirst demodulation stage 510 is the set of centroids denoted Q′^([1]).The first modulation stage 510 outputs a decision ŝ′_(k) ^([1]) which isthe centroid-based value included in Q′^([1]) that most closelycorresponds to the signal r_(k). The first demodulation stage 510 alsogenerates a re-modulated signal {circumflex over (r)}′_(k) ^([1]) as afunction of ŝ′_(k) ^([1]) and the channel 120 over which the signal iscarried as given by:{circumflex over (r)}′ _(k) ^([1]) =H ₀ ŝ′ _(k) ^([1])  (4)where H₀ represents the channel 120.

The first demodulation stage 510 removes the re-modulated signal{circumflex over (r)}′_(k) ^([1]) from r_(k) to generate a modifiedsignal r_(k) ^([1]) for input to the second stage 520 as given by:r _(k) ^([1]) =r _(k) −{circumflex over (r)}′ _(k) ^([1]()5)The modified signal r_(k) ^([1]) is then fed to the second demodulationstage 520 instead of the original signal r_(k). The second demodulationstage 520 determines the final symbol decision ŝ_(k) by demodulatingr_(k) ^([1]) output by the first stage 510 using subset Q′^([2]) ofconstellation points input to or selected by the last stage 520 togenerate a localized symbol decision ŝ′_(k) ^([2]) associated with thesecond stage 520. A summer 530 included in or associated with the seconddemodulation stage 520 sums ŝ′_(k) ^([1]) and ŝ′_(k) ^([2]) to generatethe final symbol decision ŝ_(k) as given by:ŝ _(k) =ŝ′ _(k) ^([1]) +ŝ′ _(k) ^([2])  (6)

To account for change to the input of the second demodulation stage 520,constellation Q′^([2]) is the subset of Q centered so its centroid isequal to 0. With regard to the subset embodiment shown in FIG. 4,Q′^([2]) is the middle subset. The decision s′_(k) ^([2]) output by thesecond demodulation stage 520 is an element of Q′^([2]). Consideringagain an exemplary 8-ASK constellation embodiment, Q′^([1])={−4,0,+4}and Q′^([2])={−3,−1,+1,+3}. The second subset Q′^([2)] corresponds tothe 4-ASK constellation. This SLI embodiment is referred to herein asSL34. The corresponding number of comparisons is 3 and 4, for a total of7 compared to 8 for MLD. The computational efficiency SLI has over MLDincreases substantially for MIMO and multi-code transmission scenarios.

An L×L MIMO embodiment is described next, where a plurality of signalcomponents are transmitted from multiple antennas and received frommultiple antennas. The number of transmit and receive antennas are bothassumed to be equal to L. Those skilled in the art will recognize thatthe number of receive antennas may in fact be smaller or larger than thenumber of transmit antennas. Now r_(k), s_(k) and v_(k) in equation (1)are L×1 vectors and H₀ is an L×L matrix. For ease of explanation onlyand without much loss of generality, the same constellation is presumedto be used for all L transmitted signals. However, those skilled in theart will recognize that the embodiments described next can be readilyexpanded to cover the scenario where some or all of the L transmittedsignals have different constellations. The effective constellation atthe receiver has points given by H₀ŝ_(k) and size q. Unlike the SISOcase, where the channel 120 applied a trivial scaling and rotation tothe constellation, here the effective constellation gets distorted byH₀. In principle, overlapping subsets can be designed for the effectiveconstellation. However, the effective constellation changes with thechannel 120, and thus so would the design of the overlapping subsets. Inanother embodiment, the subsets can be designed on a signal componentbasis. According to this embodiment, the discrepancy between the MLD andSLI decision boundaries can be big enough to affect performance of theSLI when the effective constellation is distorted significantly.However, this embodiment still proves to be very resilient.

Again turning to the exemplary 8-ASK constellation, the 8-ASKconstellation is applied to 2×2 MIMO in an embodiment, where each signalcomponent constellation is 8-ASK. For the 2-stage SLI structure 500shown in FIG. 5, the three overlapping subsets shown in FIG. 4 are usedfor each signal component constellation. According to the SL34embodiment, the first demodulation stage 510 compares 3×3=9 candidatesand the second demodulation stage 520 compares 4×4=16 candidates, for anSLI total of 25. In contrast, MLD compares 8×8=64 candidates. In analternate embodiment, the set of centroid-based values input to thefirst demodulation stage 510 includes four values and is given byQ′^([1])={−5,−1,+1,+5}. The subset points input to the seconddemodulation stage 520 includes three ASK localized constellation pointsgiven by Q′^([2])={−2,0,+2}. This SLI embodiment is referred to hereinas SL43. In yet another embodiment referred to herein as SL25,Q′^([1])={−3,+3} and Q′^([2])={−4,−2,0,+2,+4}. In each case, the subsetsoverlap to reduce the likelihood of errors caused by the 2-stage SLIstructures described herein. The 2-stage SLI embodiments describedherein can be readily extended to any number of desired stages.

FIG. 6 illustrates an embodiment of the i-th stage 600 of an SLIdemodulator structure where i<N. The input to the i-th demodulationstage 600 is the modified received signal r_(k) ^([i−1]) output by theimmediately preceding stage (not shown in FIG. 6). The constellationQ′^([i]) input to the i-th stage 600 includes a set of centroid-basedvalues determined as previously described herein. A MLD component 610 ofthe i-th stage 600 outputs symbols ŝ′_(k) ^([i]) based on Q′^([i]) andr_(k) ^([i−1]). A re-modulator component 620 of the i-th stage 600generates a re-modulated signal {circumflex over (r)}′_(k)^([i])=H₀ŝ′_(k) ^([i]). A signal subtractor component 630 of the i-thstage 600 subtracts {circumflex over (r)}′_(k) ^([i]) from r_(k)^([i−1]) to yield a modified received signal r_(k) ^([i]), which is fedto the next stage (not shown in FIG. 6).

FIG. 7 illustrates an embodiment of an N-stage SLI demodulationstructure 700. The input to the first stage 710 is the original receivedsignal r_(k) ^([0])=r_(k). For the last stage 730, the constellationQ′^([N]) is a subset of Q. There is no need for re-modulation block inthe last stage 730. A summer component 740 included in or associatedwith the last stage 730 determines the overall final symbol decision byadding all intermediate symbol decisions as given by:ŝ _(k) =ŝ′ _(k) ^([1]) + . . . +ŝ′ _(k) ^([N])  (7)In one embodiment, each intermediary stage 720 of the N-stage SLIdemodulator 700 has the same structure as the i-th demodulation stage600 shown in FIG. 6. According to this embodiment, the i-th intermediarystage 720 localizes the search for the final symbol decision ŝ_(k) bydemodulating a modified version of the received signal r_(k) ^([i−1])output by the immediately preceding stage using the set ofcentroid-based values Q′^([i]) input to or selected by the i-thintermediary stage 720 and outputting a localized symbol decision ŝ′_(k)^([i]) as described previously herein.

The i-th intermediary stage 720 also generates a re-modulated signal{circumflex over (r)}′_(k) ^([i]) as a function of the channel 120 andthe localized symbol decision generated by the stage 720. There-modulated signal {circumflex over (r)}′_(k) ^([i]) is removed fromthe modified version of the received signal r_(k) ^([i−1]) output by theimmediately preceding stage, e.g. as shown in FIG. 6, to generate anewly modified version of the received signal r_(k) ^([i]) for input tothe stage immediately following the i-th intermediary stage 720.Subtracting {circumflex over (r)}′_(k) ^([i]) removes part of thetransmitted signal, which acts as self-interference. This enables laterstages to operate with less self-interference. The constellationQ′^([i]) input to or selected by each of the i intermediary stages 720includes centroid-based values, which may or may not belong to Q,whereas the constellation Q′^([N]) input to or selected by the laststage 730 is a subset of Q. As such, the last stage 730 of the N-stageSLI demodulation structure 700 functions as an MLD on what is left fromthe original signal in r_(k) ^([N−1]).

Broadly, there is no restriction on how the overlapping subsets used forSLI are defined. Subset size can vary, the number of available subsetscan change from stage to stage, etc. For the case of ASK, overlappingsubsets can be defined in a way that yields a nested structure and athree subset representation. Consider the general case of 2^(L) ASK,having the constellation given by:Q={2^(L)+1, . . . ,−1,+1, . . . ,+2^(L)−1}  (8)Three overlapping subsets are defined, where the first subset containsthe 2^(L−1) negative points. The second includes the 2^(L−1) middlepoints {2^(L−1)+1, . . . ,+2^(L−1)−1}, corresponding to 2^(L−1) ASK. Thethird subset includes the 2^(L−1) positive points. The centroids foreach of the three subsets are −2^(L−1), 0 and +2^(L−1), respectively.The same technique can be used to generate three overlapping subsets for2^(L−1) ASK, and so on. An N-stage SLI demodulation structure can thenbe designed using these subsets with N≦L. Except for the last stage ofthe N-stage SLI demodulator, the set of centroids input to or selectedby the i-th stage is given by:Q′ ^([i])={−2^(N−1),0,+2^(N−1)}  (9)

The last stage of the N-stage SLI demodulator has the constellation of2^(L−N+1) ASK. In particular, for N=L−1, Q′^([N])={−3,−1,+1,+3}. If themaximum number of stages N=L is used, then Q′^([N])={−1,+1}. Againconsidering 8ASK, the SL34 structure satisfies the nested subset design.Alternatively, a 3-stage SLI demodulator structure with the nestedsubset design can also be employed where the first and seconddemodulator stages each compares 9 candidates, and the third (last)demodulator stage compares 4 candidates, for a total of 21, which isslightly less than 25 for the SL34 structure.

The SLI embodiments described herein can be readily adapted to othermodulation schemes such as QAM. The extension of SLI from ASK to QAM isstraightforward. Again, in principle, there is no restriction on how theoverlapping subsets are defined. In one embodiment, the nested subsetdesign of 2^(L)-ASK can be generalized to 2^(2L)-QAM. Just as QAM can beviewed as taking the product of two ASK constellations to produce thecomplex QAM constellation, the product of the ASK subsets can be takento produce the subsets of QAM.

FIG. 8 illustrates an embodiment of generalizing ASK to 16-QAM. Each QAMconstellation point shown in FIG. 8 is represented by an ‘X’. The threesubsets for ASK, e.g. as shown in FIG. 4, yield nine subsets for 16-QAMas illustrated by the boxes drawn around the different groups ofconstellation points in FIG. 8. At least two adjacent subsets haveoverlapping constellation points. The middle subset coincides with4-QAM, or QPSK (Quadrature Phase-Shift Keying). The nine centroid valuesfor 16-QAM, which are shown as circles in FIG. 8, are also determinedfrom the respective three centroid values for ASK. ASK can be furthergeneralized to 64-QAM. For the SL34 embodiment and 64-QAM, the firstdemodulation stage compares 9×9=81 candidates and the second demodulatorstage compares 16×16=256 candidates, for a total of 337. In contrast,MLD compares 64×64=4096 candidates for 64-QAM. Thus, thereduced-complexity advantage of SLI becomes more pronounced as theconstellation grows.

The design of overlapping subsets need not be based on the component ASKconstellation. FIG. 9 illustrates an embodiment of the 16-QAMconstellation where each of the subsets is directly determined from theQAM constellation and not derived from ASK. Each QAM constellation pointshown in FIG. 9 is represented by an ‘X’ and the subsets are shown asboxes drawn around different groups of constellation points. Again, atleast two adjacent subsets have overlapping constellation points. Eachof the SLI embodiments described herein, including subset selection,yield a low complexity alternative to MLD with good performance. SLIprovides a distinct complexity advantage as the effective modulationconstellation grows, such as in MIMO and multi-code scenarios.

With the above range of variations and applications in mind, it shouldbe understood that the present invention is not limited by the foregoingdescription, nor is it limited by the accompanying drawings. Instead,the present invention is limited only by the following claims, and theirlegal equivalents.

What is claimed is:
 1. A method of demodulating a received signalcorresponding to a transmitted signal carried over a channel,comprising: grouping points of a constellation associated with thetransmitted signal into a plurality of subsets, adjacent ones of thesubsets having one or more common constellation points so that at leasttwo adjacent subsets overlap; determining a centroid-based value foreach of the subsets of constellation points; grouping the centroid-basedvalues into one or more sets for input to a demodulator having aplurality of stages wherein a first one of the stages localizes a searchfor a final symbol decision; and demodulating the received signal usingthe demodulator, each of the stages except for a last one of the stageslocalizing the search for the final symbol decision using the set ofcentroid-based values input to or selected by the stage as constellationpoints to generate a localized symbol decision and the last stagegenerates a last one of localized symbol decisions for determining thefinal symbol decision using one of the subsets of constellation pointsinput to or selected by the last stage; and summing each of thelocalized symbol decisions generated by each of the plurality of stagesto generate the final symbol decision.
 2. The method of claim 1, whereinthe constellation associated with the transmitted signal is an effectiveconstellation determined for the channel over which the transmittedsignal is carried.
 3. The method of claim 1, wherein the constellationassociated with the transmitted signal corresponds to a constellationused to modulate the transmitted signal prior to transmission.
 4. Themethod of claim 1, wherein the transmitted signal comprises a pluralityof signal components transmitted from multiple antennas.
 5. The methodof claim 1, comprising selecting the subset of constellation points usedby the last stage of the demodulator for determining the final symboldecision based on a localized symbol decision output by the stageimmediately preceding the last stage, the localized symbol decisioncorresponding to one of the centroid-based values included in the set ofcentroid-based values input to or selected by the immediately precedingstage.
 6. The method of claim 5, comprising determining the final symboldecision based on the received signal and the subset of constellationpoints selected for the last stage of the demodulator.
 7. The method ofclaim 1, wherein determining a centroid-based value for each of thesubsets of constellation points comprises determining a centroid foreach of the subsets of constellation points.
 8. A receiver, comprising:a constellation processing module operable to group points of aconstellation associated with a transmitted signal into a plurality ofsubsets, at least two adjacent ones of the subsets having one or morecommon constellation points so that the at least two adjacent subsetsoverlap, determine a centroid-based value for each of the subsets ofconstellation points and group the centroid-based values into one ormore sets; and a plurality of demodulation stages, each of thedemodulation stages except for a last one of the demodulation stagesbeing operable to localize a search for a final symbol decision usingthe set of centroid-based values input to or selected by thedemodulation stage as constellation points to generate a localizedsymbol decision; wherein a first one of the demodulation stages isoperable to demodulate a received signal using the set of centroid-basedvalues input to the first demodulation stage to generate a first one oflocalized symbol decisions output by the first demodulation stage; andwherein the last demodulation stage generates a last one of thelocalized symbol decisions to determine the final symbol decision usingthe subset of constellation points input to or selected by the lastdemodulation stage; and a summer operable to sum each of the localizedsymbol decisions generated by each of the plurality of stages togenerate the final symbol decision.
 9. The receiver of claim 8, whereinthe constellation associated with the transmitted signal is an effectiveconstellation determined for a channel over which the transmitted signalis carried.
 10. The receiver of claim 8, wherein the constellationassociated with the transmitted signal corresponds to a constellationused to modulate the transmitted signal prior to transmission.
 11. Thereceiver of claim 8, wherein the transmitted signal comprises aplurality of signal components transmitted from multiple antennas. 12.The receiver of claim 8, wherein the last demodulation stage is operableto select the subset of constellation points for determining the finalsymbol decision based on a localized symbol decision output by thedemodulation stage immediately preceding the last demodulation stage,the localized symbol decision corresponding to one of the centroid-basedvalues included in the set of centroid-based values input to or selectedby the immediately preceding demodulation stage.
 13. The receiver ofclaim 8, wherein the last demodulation stage is operable to determinethe final symbol decision based on a received signal and the subset ofconstellation points selected by the last demodulation stage.